01 POWER ISLAND / 01 CCPP / V. Ganapathy-Industrial Boilers and HRSG-Design (2003)

or

rf is given in Fig. 7.9.

The equivalent lengths have to be obtained after considering the bends, elbows, etc., in the piping. See Tables 7.10 and 7.12.

FIGURE 7.9 Two-phase friction factor for unheated tubes. (See Refs. 11, 15, and 16.)

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TABLE 7.12 Le=di , Ratios for Fitting Turbulent

Flow

A heat balance is first done around the steam drum to estimate the amount of liquid heat to be added to the steam–water mixture before the start of boiling. The mixture is considered to be water until boiling starts.

Once all of the losses are computed, the available head is compared with the losses. If they match, the assumed circulation rate is correct; otherwise another iteration is performed. As mentioned before, this method gives an average circulation rate for a particular circuit. If there are several parallel circuits, then the CR must be determined for each circuit. The circuit with the lowest CR and highest heat fluxes should be evaluated for DNB.

In order to analyze for DNB, one may compute the allowable steam quality at a given location in the evaporator with the actual quality. The system is considered safe if the allowable quality is higher than the actual quality. The allowable quality is based on the heat flux, pressure, mass velocity, and roughness and orientation of the tubes. Studies have been performed to arrive at these values. Figure 7.10 shows a typical chart [14] that gives the allowable steam quality as a function of pressure and heat flux. It can be seen that as the pressure or heat flux increases, the allowable quality decreases. Another criterion for ensuring that a system is safe is that the actual heat flux on the steam side (inside tubes in water tube boilers and outside tubes in fire tube boilers) must be lower than the critical heat flux (CHF) for the particular conditions of pressure, flow, tube size, roughness, orientation, etc. CHF values are available in the literature; boiler manufacturers have developed their own CHF correlations based on their experience. See Chapter 8 for an example.

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FIGURE 7.10 Allowable quality for nucleate boiling at 2700 psia, as a function of mass velocity and heat flux inside tubes. (From Ref. 14.)

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7.31b

Q:

Compute the circulation ratio and check the system shown in Fig. 7.4 for DNB.

A:

Figure 7.4 shows a boiler schematic operating on natural circulation principles. The basis for estimating the flow through water walls is briefly as follows.

1.Assume a circulation ratio (CR) based on experience. For low pressure boilers ( < 1000 psia), CR could be from 20 to 50. For high pressure boilers (1000–2700 psia), CR could range from 9 to 5. The following expression relates circulation ratio and dryness fraction, x:

Hence, flow through the evaporator ¼ CR the steam generated.

2.Furnace thermal performance data such as efficiency, furnace exit temperature, and feedwater temperature entering the drum should be known before the start of this exercise, in addition to details such as the location of the drum, bends, size, and length of various circuits.

3.Mixture enthalpy entering downcomers is calculated as follows through an energy balance at the drum.

4.As the flow enters the water walls, it gets heated, and boiling starts after a particular distance from the bottom of the furnace. This distance is called boiling height, and it increases as the subcooling increases. It is calculated as follows.

Lb ¼ L CR Ws hf hm

Q

Beyond the boiling height, the two-phase flow situation begins.

5.Friction loss in various circuits such as downcomers, connecting headers, water wall tubes (single-phase, two-phase losses), riser

pipes, and drums are calculated. Gravity losses, DPg, are estimated along with the acceleration losses, DPa, in a boiling regime. The head available in the downcomer is calculated and equated with the losses. If they balance, the assumed CR is correct; otherwise, a revised trial is made until they balance. Flow through the water wall tubes is thus estimated.

6.Checks for DNB are made. Actual quality distribution along furnace height is known. Based on the heat flux distribution (Fig. 7.11), the

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FIGURE 7.11 Typical heat absorption rates along furnace height.

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allowable quality along the furnace height can be found. If the allowable quality exceeds actual quality, the design is satisfactory; otherwise, burnout possibilities exist, and efforts must be made to improve the flow through water wall tubes.

Example

A coal-fired boiler has a furnace configuration as shown in Fig. 7.4. Following are the parameters obtained after performing preliminary thermal design:

Because it is difficult to estimate flow through parallel paths, let us assume that flow in each tube or circuit of downcomers, water walls, and risers may be near the average flow values. However, computer programs may be developed that take care of different circuits. The manual method gives a good idea of the solution procedure (though approximate).

Method

Let circulation ratio CR ¼ 8. Then x ¼ 0.125. From the steam tables,

tsat ¼ 680 F

hg ¼ 1069.7 Btu=lb hf ¼ 753.7 Btu=lb vf ¼ 0.0303 cu ft=lb vg ¼ 0.112 cu ft=lb hfw ¼ 568 Btu=lb

Enthalpy of steam leaving water walls is

he ¼ 0:125 1069:7 þ 0:875 753:7 ¼ 793:2 Btu=lb

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Heat balance around the drum gives

Steam flow ¼ 600;000 lb=h

Water wall, downcomer flow ¼ 8 600;000

¼ 4;800;000 lb=h

600;000 568 þ 8 600;000 793:2 ¼

600;000 1069:7 þ 8 600;000 hm

Hence, hm ¼ 731 Btu=lb.

From the steam tables,

vm ¼ 0:0286 cu ft=lb

ve ¼ 0:125 0:112 þ 0:875 0:0303

¼0:0405 cu ft=lb

a.DPg ¼ head available ¼ 106=ð0:0286 144Þ ¼ 25:7 psi.

b.DPdc ¼ losses in downcomer circuit.

The downcomer has one 90 bend and one entrance and exit loss. Using an approximate equivalent length of 7di,

Le ¼ 104 þ 16 þ ð7 12Þ ¼ 204 ft

The value fi from Table 7.6 is around 0.013.

0:013 204 ð12:1Þ2 12 DPdc ¼ 2 32 12 0:0286 144

¼1:47 psi

c.Estimate boiling height:

753:7 731 Lb ¼ 100 8 600;000 320 106

¼ 31 ft

Hence, up to a height of 31 ft, preheating of water occurs. Boiling occurs over a length of only 100 7 31 ¼ 69 ft.

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d.Gravity loss in boiling height:

Vm; mean specific volume ¼ 0:0286 þ 0:0303 2

¼ 0:02945 cu ft=lb

31

DPg ¼ 0:02945 144 ¼ 7:3 psi

e.Friction loss in boiling height. Compute velocity through water wall tubes: di ¼ 2.1 in.

8 600;000 576 0:02945 Vw ¼ 416 p ð2:1Þ2 3600

¼ 3:93 fps

From Table 7.6, fi ¼ 0.019.

One exit loss, one 135 bend, and one 45 bend can be considered for computing an equivalent length. Le works out to about 45 ft.

0:019 45 ð3:93Þ2 12 DPw ¼ 2 32 2:1 0:02945 144

¼0:28psi

f.Compute losses in two-phase flow, from Figs. 7.6–7.8, for x ¼ 12:5% and P ¼ 2700 psi,

¼ 0:5 psi

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Total two-phase loss ¼ 0:026 þ 0:5 þ 13:4

¼13.926 psi, or 14.0 psi

g.Riser circuit losses. Use Thom’s method for two-phase unheated tubes. Let the total equivalent length, considering bends and inlet and exit losses, be 50 ft.

Note that in estimating pressure drop by Thom’s method for heated tubes, the Darcy friction factor was used. For unheated tubes, Moody’s

1445 ¼ 0:85 psi

Total losses in riser circuit ¼ 1.41 þ 0.85 ¼ 2.26 psi.

h.Losses in drum. This is a negligible value; use 0.2 psi. (Generally the supplier of the drums should furnish this figure.)

Total losses ¼ b þ d þ e þ f þ g þ h

¼1:47 þ 7:3 þ 0:28 þ 14:0 þ 2:26 þ 0:2

¼25:51 psi

Available head ¼ a ¼ 25:7 psi

Hence, because these two match, an assumed circulation ratio of 8 is reasonable. This is only an average value for the entire system. If one is interested in a detailed analysis, the circuits should be separated

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FIGURE 7.12 Void fraction as a function of quality and pressure for steam [See Refs. 11, 16].

according to heat loadings, and a rigorous computer analysis balancing flows and pressure drop in each circuit can be carried out.

Analysis for DNB

Typical furnace absorption profiles for the actual fuel fired are desirable for DNB analysis. These data are generally based on field tests, but for the problem at hand let us use Fig. 7.11, which gives typical absorption profiles for a boiler.

¼ 38,095 Btu/ft2 h

There is a variation at any plan cross section of a boiler furnace between the maximum heat flux and the average heat flux, based on the burner location, burners in operation, excess air used, etc. This ratio between maximum and average could be 20–30%. Let us use 25%.

Again, the absorption profile along furnace height shows a peak at some distance above the burner where maximum heat release has occurred. It decreases as the products of combustion leave the furnace. The average for the entire profile

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